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There are a few excellent suggested builds (Sivir, for example). There are also some pretty terrible suggested builds.

In general, here are some of the best items available:

DPS -
Infinity Edge - Gives massive damage and even more massive criticals, best increase to DPS of any item in the game
Last Whisper - % Penetration makes standard counters to DPS (Armor stacking) ineffective. This item combined with Infinity Edge forms the core of almost every DPS build.
Bloodthirster - Single biggest boost to Lifesteal and one of the largest boosts to attackdamage, this is a great damage item, especially on characters who have abilities that scale with damage.
Stark's Fervor - Gives a lot of useful stats and gives them to everyone on the team, making the item very effective.
Frozen Mallet - gives a slow and a lot of survivability

AP -
Mejai's Soulstealer - Considered a must have for most AP builds, as it gives by far the largest AP boost of any single item.
Void Staff - AP Version of last whisper
Zhonya's Ring - Gives a huge AP boost and the ability to evade focusing
Rylai's Crystal Scepter - Gives a slow and a lot of survivability
Deathfire Grasp - Provides another Nuke
Lichbane - turns autoattack into an AP-scaling nuke

Tank -
Aegis of the Legion - Only item that gives HP, Armor, and MR, fairly cheap, and provides a bonus to the entire team
Warmogg's Armor - Biggest boost to HP in the game
Banshee's Veil - Provides a huge boost to HP and MR as well as straight-out blocking spells.
Force of Nature - Biggest MR item in the game, also gives a ton of regen and movespeed
Guardian Angel - Fulfill your role as initiator best by not even dying when focused down
Thornmail - Biggest Armor item in the game